

A059086


Number of labeled T_0hypergraphs with n distinct hyperedges (empty hyperedge included).


7




OFFSET

0,1


COMMENTS

A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.


LINKS



FORMULA

a(n) = (1/n!)*Sum_{k = 0..n} stirling1(n, k)*floor((2^k)!*exp(1)).


EXAMPLE

a(2)=30; There are 30 labeled T_0hypergraphs with 2 distinct hyperedges (empty hyperedge included): 1 1node hypergraph, 5 2node hypergraphs, 12 3node hypergraphs and 12 4node hypergraphs.
a(3) = (1/3!)*(2*[2!*e]3*[4!*e]+[8!*e]) = (1/3!)*(2*53*65+109601) = 18236, where [k!*e] := floor (k!*exp(1)).


MAPLE

with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d, `, (1/n!)*sum(stirling1(n, k)*floor((2^k)!*exp(1)), k=0..n)) od:


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



